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Estimating medical costs from a transition model

Joseph C. Gardiner, Lin Liu, and Zhehui Luo

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Nonparametric estimators of the mean total cost have been proposed in a variety of settings. In clinical trials it is generally impractical to follow up patients until all have responded, and therefore censoring of patient outcomes and total cost will occur in practice. We describe a general longitudinal framework in which costs emanate from two streams, during sojourn in health states and in transition from one health state to another. We consider estimation of net present value for expenditures incurred over a finite time horizon from medical cost data that might be incompletely ascertained in some patients. Because patient specific demographic and clinical characteristics would influence total cost, we use a regression model to incorporate covariates. We discuss similarities and differences between our net present value estimator and other widely used estimators of total medical costs. Our model can accommodate heteroscedasticity, skewness and censoring in cost data and provides a flexible approach to analyses of health care cost.

Chapter information

N. Balakrishnan, Edsel A. Peña and Mervyn J. Silvapulle, eds., Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 350-363

First available in Project Euclid: 1 April 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 62N01: Censored data models 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 62G05: Estimation

censoring Kaplan-Meier estimator longitudinal data Markov model inverse-weighting random-effects

Copyright © 2008, Institute of Mathematical Statistics


Gardiner, Joseph C.; Liu, Lin; Luo, Zhehui. Estimating medical costs from a transition model. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 350--363, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000266.

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  • [1] Andersen, P. K., Borgan, O., Gill, R. D. and Keiding, N. (1993). Statistical Models Based on Counting Processes. Springer, New York.
  • [2] Bang, H. and Tsiatis, A. A. (2000). Estimating medical costs with censored data. Biometrika 87 329–343.
  • [3] Bang, H. and Tsiatis, A. A. (2002). Median regression with censored cost data. Biometrics 58 643–649.
  • [4] Baser, O., Gardiner, J. C., Bradley, C. J. and Given, C. W. (2004). Estimation from censored medical cost data. Biometrical Journal 46 351–363.
  • [5] Baser, O., Gardiner, J. C., Bradley, C. J., Yuce, H. and Given, C. (2006). Longitudinal analysis of censored medical cost data. Health Economics 15 513–525.
  • [6] Chen, P. L. and Sen, P. K. (2001). Quality-adjusted survival estimation with periodic observations. Biometrics 57 868–874.
  • [7] Chen, P. L. and Sen, P. K. (2004). Quality-adjusted survival estimation with periodic observations: A multistate survival analysis approach. Comm. Statist. Theory Methods 33 1327–1339.
  • [8] Gardiner, J. C., Luo, Z., Bradley, C. J., Sirbu, C. M. and Given, C. W. (2006a). A dynamic model for estimating changes in health status and costs. Statistics in Medicine 25 3648–3667.
  • [9] Gardiner, J. C., Luo, Z., Liu, L. and Bradley, C. J. (2006b). A stochastic framework for estimation of summary measures in cost-effectiveness analyses. Expert Review of Pharmacoeconomics and Outcomes Research 6 347–358.
  • [10] Henderson, R., Diggle, P. and Dobson, A. (2000). Joint modelling of longitudinal measurements and event time data. Biostatistics 1 465–480.
  • [11] Hogan, J. W. and Laird, N. M. (1997a). Mixture models for the joint distribution of repeated measures and event times. Statistics in Medicine 16 239–257.
  • [12] Hogan, J. W. and Laird, N. M. (1997b). Model-based approaches to analysing incomplete longitudinal and failure time data. Statistics in Medicine 16 259–272.
  • [13] Lin, D. Y. (2000). Linear regression of censored medical costs. Biostatistics 1 35–47.
  • [14] Lin, D. Y. (2003). Regression analysis of incomplete medical cost data. Statistics in Medicine 22 1181–1200.
  • [15] Lin, D. Y., Feuer, E. J., Etzioni, R. and Wax, Y. (1997). Estimating medical costs from incomplete follow-up data. Biometrics 53 419–434.
  • [16] Norberg, R. (1995). Differential-equations for moments of present values in life-insurance. Insurance Mathematics and Economics 17 171–180.
  • [17] O’Hagan, A. and Stevens, J. W. (2004). On estimators of medical costs with censored data. Journal of Health Economics 23 615–625.
  • [18] Strawderman, R. L. (2000). Estimating the mean of an increasing stochastic process at a censored stopping time. Journal of the American Statistical Association 95 1192–1208.
  • [19] Willan, A. R., Lin, D. Y., Cook, R. J. and Chen, E. B. (2002). Using inverse-weighting in cost-effectiveness analysis with censored data. Statistical Methods in Medical Research 11 539–551.
  • [20] Wooldridge, J. M. (2002). Econometric Analysis of Cross Section and Panel Data. MIT Press, Cambridge, MA.
  • [21] Zhao, H. W. and Tian, L. L. (2001). On estimating medical cost and incremental cost-effectiveness ratios with censored data. Biometrics 57 1002–1008.